Theoretical and methodological framework for the study of the limit

Our research covers, with the same methods, several notions of limits, as the finite limit of a sequence or the finite limit of a function in a point. We consider three related elements: phenomenology, representation systems, and advanced mathematical thinking. In the first part we explain this and we also present ideas from other theoretical frameworks. We have been using the same methodological tools to uncover and study phenomena organized by three cases of finite limit and to recognize these phenomena in textbooks. Besides this we have developed tools to show those phenomena used by students and teachers. In the second part we describe the methods used to extract information from textbooks and students.